作者dn890221 (车)
看板trans_math
标题Re: [考古] 95年台大B第三题瑕积分
时间Thu Jun 24 16:34:47 2010
※ 引述《skyword (天)》之铭言：
3.
∞ lnx
∫ ----- dx = ?
1 n
x
我知道当n>1的时候收敛
但是他的积分值该怎麽算?
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 219.84.252.23
※ 编辑: skyword 来自: 219.84.252.23 (06/02 12:13)
1F：→ GLP:分部积分吧@@ 219.70.171.81 06/02 15:19
2F：→ OKOK98:把x分之1丢到後面去就结束了140.114.216.145 06/02 15:37
3F：→ skyword:这分部积分不是分到死吗@@ 219.84.252.23 06/02 16:32
4F：→ skyword:回ok大 可是她是X^n次耶 剩下来的怎麽办? 219.84.252.23 06/02 16:33
5F：→ OKOK98:欧...看错了 n大於1喔 我看成等於1 sorry140.114.216.145 06/02 16:34
6F：→ GLP:积一次即口 219.70.171.81 06/02 16:39
7F：→ OKOK98:LP大说得没错~~140.114.216.145 06/02 16:45
8F：→ skyword:积一次..?不太懂这个意思 219.84.252.23 06/02 18:01
我把它分部积分之後的结果是这样
-ln(x) 1 |∞
-------------- - --------------- |
n-1 2 n-1 |
(n-1) * x (n-1) * x |1
-ln(b) 1 1
lim -------------- - --------------- - --------
b→∞ n-1 2 n-1 2
(n-1) * b (n-1) * b (n-1)
所以积分值是 -1 / (n-1)^2吗?
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my skill and knowledge shall be given without reservation for the public good.
In the performance of duty and in fidelity to my profession, I shall give the
utmost.
excerpt from: The Obligation of an Engineer dn890221
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 140.112.202.116
9F：推 midarmyman:我算是正的耶 140.117.198.78 06/24 19:14
10F：推 midarmyman:你最後一项 应该是加? 140.117.198.78 06/24 19:17
11F：→ dn890221:啊对 是+的140.112.202.116 06/24 19:32
12F：推 s23325522:积分审练~140.115.213.154 06/25 15:58